N-Bishop Darboux Vector of a Timelike Curve in Minkowski 3-Space

Samanci, Hatice Kusak

doi:10.46939/j.sci.arts-20.3-a02

Cited by 4 publications

(3 citation statements)

References 13 publications

(15 reference statements)

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“…In [12], Ugail, Marquaez and Yılmaz handled the conditions of timelike and spacelike Bézier surfaces. The Serret-Frenet frames, curvatures and torsion of the timelike and spacelike Bézier curves were calculated at the end points in [13][14][15][16]. Our aim in this paper is to investigate the timelike and spacelike Bézier curve of degree m at all points.…”

Section: Introductionmentioning

confidence: 99%

The Geometry of Bezier Curves in Minkowski 3−Space

Ceylan

2023

Universal Journal of Mathematics and Applications

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Section: Introductionmentioning

confidence: 99%

The Geometry of Bezier Curves in Minkowski 3−Space

Ceylan

2023

Universal Journal of Mathematics and Applications

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“…Then, Kus ¸ak Samancı (2018a, b, c, d) researched the Bezier, space-like rational Bezier, timelike rational Bezier, and the timelike uniform B-spline curves in Minkowski 3-space. Moreover,Kus ¸ak Samancı et al (2019) studied some properties concerning the timelike Bezier curves. Erkan and Y€ uce (2018) studied the curvature of the Bezier curves and the Serret-Frenet frame.…”

Section: Introductionmentioning

confidence: 99%

The quasi-frame of the rational and polynomial Bezier curve by algorithm method in Euclidean space

Samanci

2023

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PurposeFrames play an important role in determining the geometric properties of the curves such as curvature and torsion. In particular, the determination of the point types of the curve, convexity or concavity is also possible with the frames. The Serret-Frenet frames are generally used in curve theory. However, the Serret-Frenet frame does not work when the second derivative is zero. In order to eliminate this problem, the quasi-frame was obtained. In this study, the quasi frames of the polynomial and rational Bezier curves are calculated by an algorithmic method. Thus, it will be possible to construct the frame even at singular points due to the second derivative of the curve. In this respect, the contribution of this study to computer-aided geometric design studies is quite high.Design/methodology/approachIn this study, the quasi frame which is an alternative for all intermediate points of the rational Bezier curves was generated by the algorithm method, and some variants of this frame were analyzed. Even at the points where the second derivative of such rational Bezier curves is zero, there is a curve frame.FindingsSeveral examples presented at the end of the paper regarding the quasi-frame of the rational Bezier curve, polynomial Bezier curve, linear, quadratic and cubic Bezier curves emphasize the efficacy and preciseness.Originality/valueThe quasi-frame of a rational Bezier curve is first computed. Owing to the quasi frame, it will have been found a solution for the nonsense rotation of the curve around the tangent.

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“…Harmonic evolute surface of quasi binormal surface associated with quasi frame was studied [1]. The N-Bishop frame for timelike curves in Minkowski space was investigated [2]. Authors defined Fermi-Walker derivative in Galilean space Fermi-Walker transport and non-rotating frame by using Fermi-Walker derivative were given [3].…”

Section: Introductionmentioning

confidence: 99%